It promptly did nothing. After a few more clicks, open in new tabs and general 'what' moments, I pulled open the e-mails source, and discovered the 'Unsubscribe' link was just pointed at '#'. Not a real link at all.
Is this new? Do companies just add this button to look respectable, but in reality ensure you can't leave their mailing list?
Fortunately for myself, I gave them a temporary address on my domain..